Abstract
We present a systematic, perturbative method for correcting quantum gates to suppress errors that take the target system out of a chosen subspace. It addresses the generic problem of non-adiabatic errors in adiabatic evolution and state preparation, as well as general leakage errors due to spurious couplings to undesirable states. The method is based on the Magnus expansion: by correcting control pulses, we modify the Magnus expansion of an initially-given, imperfect unitary in such a way that the desired evolution is obtained. Applications to adiabatic quantum state transfer, superconducting qubits and generalized Landau-Zener problems are discussed.
Highlights
The problem of leakage errors, where a quantum gate is corrupted by populating spurious states, is generic to a variety of situations in quantum information processing
Control sequences designed to implement a given unitary evolution can give rise to transitions out of the logical subspace. Such “leakage errors” generically become more prominent as gates are made faster because of the increased bandwidth of control pulses. Another generic example of leakage errors comes from protocols utilizing adiabatic evolution, where, e.g., one attempts to have a system remain in the instantaneous ground state of some time-dependent Hamiltonian
We show that the approach can yield advantages over standard derivative removal by adiabatic gate (DRAG) corrections
Summary
The problem of leakage errors, where a quantum gate is corrupted by populating spurious states, is generic to a variety of situations in quantum information processing. Such “leakage errors” generically become more prominent as gates are made faster because of the increased bandwidth of control pulses (and consequent enhanced spectral weight at the frequencies of unwanted transitions) Another generic example of leakage errors comes from protocols utilizing adiabatic evolution, where, e.g., one attempts to have a system remain in the instantaneous ground state of some time-dependent Hamiltonian. We present an extremely general strategy for mitigating leakage errors In certain limits, it captures aspects of both DRAG and STA approaches, but it is able to deal with situations where these methods fail or become impossible to implement. Most Magnus-based approaches for improved controls rely on using the first term of the expansion and viewing this as a Fourier transform integral; one corrects pulses to suppress spectral weight associated with unwanted leakage transitions [22,23]. The multiple-crossings LandauZener model demonstrates how the Magnus approach can correct a complex adiabatic evolution problem for which STA techniques cannot be implemented
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